In the field of radio communications using high frequencies, signals having specific frequencies are extracted from a number of signals, so that necessary signals and unnecessary signals are separated from each other. Circuits having such a function are called filters and are installed in various radio communication devices.
Generally, filters have invariable bandwidths as design parameters. When using various frequency bandwidths in radio communication devices using such filters, it may easily occur that a plurality of filters are prepared for those bandwidths to be used and are switched by switches and so on. This method requires filters as many as required number of bandwidths and thus increases the scale of the circuit, resulting in a large device size. Further, such devices cannot be operated at frequencies other than frequencies having the frequency characteristics of prepared filters.
In order to solve this problem, in Patent literature 1, a piezoelectric element is used for a resonator composing a filter and the frequency characteristics of the piezoelectric element are changed by applying a bias voltage to the piezoelectric element from the outside, so that the bandwidth is changed.    Patent literature 1: Japanese Patent Application Laid-Open No. 2004-7352
Although the variable filter disclosed in Patent literature 1 is formed as a ladder filter to provide a certain bandwidth, a change in the center frequency is as small as under 1%, due to restrictions imposed by the characteristics of the piezoelectric element, allowing change in the bandwidth to a similar extent, so that the bandwidth cannot be largely changed.